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Full text of "Treatise On Analysis Vol-Ii"

NOTATION       xi

«?TR(X)                                              space  of continuous real-valued func-

tions on X with compact support: 13.2

/Z                                                    conjugate of the measure m 13.2

MR(X)                                          space of real measures on X: 13.2

0t\ji, Jp                                         real and imaginary parts of a complex

measure: 13.2

M+(X)                                          set of positive measures on X: 13.3

/+,/~                                         positive and negative parts of a real-

valued function/: 13.3
jU^v                                           order relation between real measures:

13.3
\\JL\                                                   absolute value of a complex measure:

13.3
*/, ./(X)                                        set of lower semicontinuous functions on

X which are bounded below by a function

belonging to JfR(X): 13.5

/<*(/), JV*. JVC*) *C*)            upper integral of/: 13.5

J] tn                                              sum of a sequence (ttt) of elements ^0 of

5: 13.5
£fy «^(X)                                       set of upper semicontinuous functions on

X which are bounded above by a function

belonging to ^TR(X): 13.5

/**(/), J*/<fo J*/C*) <W*)            lower integral of/: 13.5

jU*(A), /i*(A)                                  outer and inner measures of A c X: 13.5

/                                                   equivalence class of /(with respect to ^) :

13.6
f^g                                           order    relation    between    equivalence

classes: 13.6
f+$>f3                                        sum and product of equivalence classes :

13.6

)» </> /*>                                integral of a ju-integrable function: 13.7

J5fR(X, /i), J5fi(jw), jSf R                      space of (finite) real-valued /x-integrable

functions: 13.7

measure of a ju-integrable set: 13.7
integral of an equivalence class: 13.7
> JA/C*) *C*)                       integral of/ over A : 13.9

upper integral of /over A: 13.9

.                              measure induced by ju on a closed sub-

space Y: 13.9n the compact